Typically, a strain wave gearing has a rigid internally toothed gear, a flexible externally toothed gear disposed coaxially within the internally toothed gear, and a wave generator fitted within the externally toothed gear. A flat strain wave gearing comprises an externally toothed gear having a flexible cylindrical outer-peripheral surface on which external teeth are formed. The flexible externally toothed gear of a cup-shaped or top-hat-shaped strain wave gearing comprises a flexible cylindrical barrel part, a diaphragm extending radially from the trailing end of the cylindrical barrel part, and external teeth formed on the outer-peripheral surface portion of the cylindrical barrel part on the side facing the leading end opening. In a traditional strain wave gearing, the circular flexible externally toothed gear is ellipsoidally flexed by the wave generator, and both ends of the ellipsoidally flexed flexible externally toothed gear along the major-axis direction mesh with the rigid internally toothed gear.
Since its invention by C. W. Musser (Patent Document 1), the strain wave gearing has been contrived in a variety of inventions and designs by many researchers including the present inventor, as well as Musser himself. There are even a variety of inventions related merely to the tooth profile of strain wave gearings. In Patent Document 2, the present inventor proposed using the basic tooth profile as an involute tooth profile, and in Patent Documents 3 and 4 proposed using a technique in which a rack is used to approximate the meshing of the teeth of a rigid internally toothed gear and a flexible externally toothed gear as a tooth-profile-designing method for deriving an addendum tooth profile for both gears, which have a large area of contact.
However, in cup-shaped and top-hat-shaped strain wave gearings, the degree of flexing along the tooth trace direction of the tooth parts of the ellipsoidally flexed flexible externally toothed gear, from the side of the diaphragm toward the leading end opening, varies substantially in proportion with respect to the distance from the diaphragm. Individual portions of the tooth parts of the flexible externally toothed gear undergo repeated radially outward and inward flexing as the wave generator rotates. Thus far, no rational method for setting the tooth profile in consideration of such flexing action (coning) of the externally toothed gear caused by the wave generator has been adequately considered.
In Patent Document 5, the present inventor proposed a strain wave gearing comprising a tooth profile that enabled continuous meshing in consideration of coning of the teeth. In the strain wave gearing proposed in Patent Document 5, a desired transverse cross-section of the flexible externally toothed gear in the tooth trace direction is taken as a main cross-section, and, in a position on the major axis of an ellipsoidal rim-neutral curve of the externally toothed gear in the main cross-section, the degree of flexing 2 κmn (where κ is a flexing coefficient, m is a module, and n is a positive integer) with respect to a rim-neutral circle prior to flexing is set such that flexing occurs in a non-deflected state at 2mn (κ=1).
Rack meshing is used to approximate meshing between the externally toothed gear and the internally toothed gear, movement loci of the teeth of the externally toothed gear in relation to the teeth of the internally toothed gear accompanying rotation of the wave generator are determined in a transverse cross-section at each tooth-trace-direction position of the externally toothed gear that includes the main cross-section, and the basic tooth profile of the addenda of the internally toothed gear and the externally toothed gear is set by utilizing a curved portion from the apex point to the subsequent bottom point of a non-deflected movement locus obtained in the main cross-section.
In addition, in the tooth profile of the externally toothed gear, the tooth profile portions on both tooth-trace-direction sides of the main cross-section are modified so that negative-deflection movement loci obtained in transverse cross-sections that are closer to the diaphragm than is the main cross-section and in which flexing occurs in a negative-deflection state (flexing coefficient κ<1) and positive-deflection movement loci obtained in transverse cross-sections that are closer to the leading end opening than is the main cross-section and in which flexing occurs in a positive deflection state (flexing coefficient κ>1) describe curves that are tangent to each of the bottom and the apex of the non-deflected movement locus in the main cross-section.
In a strain wave gearing in which the tooth profile is formed in this manner, not only do the addendum tooth profiles of both the external teeth and the internal teeth continuously mesh across a wide area in the main cross-section of both gears, but it is also possible to achieve effective meshing of the addendum tooth profiles of both the external teeth and the internal teeth in the entire area along the tooth trace direction. Accordingly, it is possible to transmit a greater amount of torque than is possible with conventional strain wave gearings in which meshing occurs in a narrow tooth trace area.